However, a wide variety of untapped metrics [1]}, [2]} exist that can be used to compare and emphasize key features of interest.
In this regard, we extended the Wasserstein distance beyond the popular WGAN with the gradient penalty (WGAN-GP), which is constrained to \(l_2\)  norms and rather adapted a more complete space called the Banach space [3]}. Our technique, similar to [4]}, [5]}, [3]} shows that the characterisation of \(\gamma \) -lipschitz functions via the norm of the differential can be extended from the \(l_2\)  setting to arbitrary Banach spaces by considering the gradient as an element in the dual of \(B\) .
Such a loss function is given as:
\(\begin{aligned}L_{B} =\lambda E_{Y}\bigg ( \frac{1}{\gamma } \left\Vert  \partial D(Y)\right\Vert _B^* - 1\bigg )^2 ,\end{aligned}\) 
